
Legend:  Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
 Student Expectations (TEKS) identified by TEA are in bolded, black text.
 Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
 Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
 Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
 Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a
strikethrough.

Legend:  Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
 Unitspecific clarifications are in italicized, blue text.
 Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
 A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.

7.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


7.1A 
Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:
 Mathematical problem situations within and between disciplines
 Everyday life
 Society
 Workplace
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:

7.1B 
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
Process Standard

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving process and the reasonableness of the solution
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

7.1C 
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
Process Standard

Select
TOOLS, INCLUDING PAPER AND PENCIL AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:
 Appropriate selection of tool(s) and techniques to apply in order to solve problems
 Tools
 Paper and pencil
 Technology
 Techniques
 Mental math
 Estimation
 Number sense
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 VIII. Problem Solving and Reasoning

7.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Graphs
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.1E 
Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Representations of mathematical ideas
 Organize
 Record
 Communicate
 Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
 Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.1F 
Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Mathematical relationships
 Connect and communicate mathematical ideas
 Conjectures and generalizations from sets of examples and nonexamples, patterns, etc.
 Current knowledge to new learning
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:

7.1G 
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:
 Mathematical ideas and arguments
 Validation of conclusions
 Displays to make work visible to others
 Diagrams, visual aids, written work, etc.
 Explanations and justifications
 Precise mathematical language in written or oral communication
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing fluency with rational numbers and operations to solve problems in a variety of contexts
 Representing and applying proportional relationships
 Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
 Comparing sets of data
 TxCCRS:
 IX. Communication and Representation

7.6 
Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is expected to:


7.6G 
Solve problems using data represented in bar graphs, dot plots, and circle graphs, including parttowhole and parttopart comparisons and equivalents.
Readiness Standard

Solve
PROBLEMS USING DATA REPRESENTED IN BAR GRAPHS, DOT PLOTS, AND CIRCLE GRAPHS, INCLUDING PARTTOWHOLE AND PARTTOPART COMPARISONS AND EQUIVALENTS
Including, but not limited to:
 Graph – a visual representation of the relationships between data collected
 Organization of data used to interpret data, draw conclusions, and make comparisons
 Data – information that is collected about people, events, or objects
 Categorical data – data that represents the attributes of a group of people, events, or objects
 May represent number or ranges of numbers
 Numerical data – data that represents values or observations that can be measured and placed in ascending or descending order
 Can be counted (discrete) or measured (continuous)
 Limitations
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Fractions
 Percents converted to equivalent decimals or fractions for multiplying or dividing
 Data representations
 Bar graph – a graphical representation to organize data that uses solid bars that do not touch each other and scaled axis to show the frequency (number of times) that each category occurs
 Characteristics of a bar graph
 Titles, subtitles, and labels
 Title represents the purpose of collected data
 Subtitles clarify the meaning of the data represented on each axis
 Labels identify each category
 Representation of categorical data
 Bars
 Placed in a horizontal or vertical linear arrangement to represent data
 Solid bars that are equal in width
 Independent bars that do not touch
 Length of the bar represents the distance from zero on the axis scale
 Axis
 Represented as a number line
 Scale intervals proportionally displayed
 Intervals of one or more units
 Every piece of data represented using a onetoone or scaled correspondence as indicated by the intervals on the axis
 Value of the data represented by the bar
 Determined by reading the number on the scaled axis associated with the length of the bar
 Represents the frequency for that category
 Dot plot – a graphical representation to organize small sets of data that uses dots (or Xs) and an axis to show the frequency (number of times) that each number occurs
 Characteristics of a dot plot
 Titles, subtitles, and labels
 Title represents the purpose of collected data
 Subtitle clarifies the meaning of number line
 Labels identify each numerical increment below the line
 Representation of numerical data
 Dots (or Xs)
 Placed in a horizontal or vertical linear arrangement
 Vertical graph beginning at the bottom and progressing up above the line
 Horizontal graph beginning at the left and progressing to the right of the line
 Spaced approximately equal distances apart within each category
 Axis
 Numerical data represented by a number line labeled with proportional increments
 Every piece of data represented using a onetoone or scaled correspondence, as indicated by the key
 Dots (or Xs) generally represent one count
 May represent multiple counts if indicated with a key
 Value of the data in each category
 Determined by the number of dots (or Xs) or total value of dots (or Xs), as indicated by the key if given
 Represents the frequency for that category
 Density of dots relates to the frequency distribution of the data
 Shape of the dot plot may be used to compare shape, spread, and center of data
 Circle graph – a circular graph with partitions (sections) that represent a part of the total
 Characteristics of a circle graph
 Titles and labels
 Title represents the purpose of collected data
 Labels identify each category
 Representation of categorical data
 Partitioned circle
 Size of each partition is proportional to the magnitude of the quantity and its relationship to the 360° of the circle
 Partitions generally labeled as percents or fractions..
 Labeled as percents, sum of the quantities of the partitions is 100%
 Labeled as fractions, sum of the quantities of the partitions is 1
 Proportional relationships within data representations
 Parttowhole comparisons and equivalents
 Parttopart comparisons and equivalents
Note(s):
 Grade Level(s):
 In previous grades, students have represented data with pictographs, bar graphs, frequency tables, dot plots, stemandleaf plots scatterplots, histograms, box plots, relative frequency tables, and percent bar graphs.
 Grade 7 introduces solving problems using data represented in bar graphs, dot plots, and circle graphs, including parttowhole and parttopart comparisons and equivalents.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Representing and applying proportional relationships
 TxCCRS:
 I. Numeric Reasoning
 VI. Statistical Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

7.12 
Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data. The student is expected to:


7.12A 
Compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads.
Readiness Standard

Compare
TWO GROUPS OF NUMERIC DATA USING COMPARATIVE DOT PLOTS OR BOX PLOTS BY COMPARING THEIR SHAPES, CENTERS, AND SPREADS
Including, but not limited to:
 Graph – a visual representation of the relationships between data collected
 Organization of data used to describe and summarize data
 Data – information that is collected about people, events, or objects
 Numerical data – data that represents values or observations that can be measured and placed in ascending or descending order
 Can be counted (discrete) or measured (continuous)
 Limitations
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Fractions
 Percents
 Data representations
 Dot plot – a graphical representation to organize small sets of data that uses dots (or Xs) and an axis to show the frequency (number of times) that each number occurs
 Comparative dot plots – a graphical representation that consists of at least two related dot plots
 Characteristics of a comparative dot plot
 Display of two dot plots of the same variable from two different data sets
 Backtoback graphs with the scale in the middle
 Dots (or Xs) for one data set recorded above or to the right of the scale and dots (or Xs) for the other data set recorded below or to the left of the scale
 Every piece of data represented using a onetoone or scaled correspondence, as indicated by the key
 Dots (or Xs) generally represent one count
 May represent multiple counts if indicated with a key
 Value of the data in each category
 Determined by the number of dots (or Xs) or total value of dots (or Xs), as indicated by the key if given
 Represents the frequency for that category
 Density of the dots relates to the frequency distribution of the data
 Shape of the dot plot may be used to compare the shape, spread, and center of data, including mode, range, and outliers between and among multiple data sets
 Box plot (box and whisker plot) – a graphical representation showing the fivenumber summary of data (minimum, lower quartile, median, upper quartile, maximum)
 Comparative box plots – a graphical representation that consists of at least two related box plots
 Characteristics of a comparative box plot
 Display of two box plots of the same variable from two different data sets
 Two box plots, each representing a different data set, stacked one above the other with the scale below both box plots; or two box plots, each representing a different data set, with the scale in between the two box plots
 Density of quartiles represents the frequency distribution of the data
 Shape of the box plot may be used to compare the spread of the data, including median (center), upper and lower extremes, quartiles, interquartile range (IQR), and range between and among multiple data sets
 Measures of center of a data distribution
 Mean – average of a set of data found by finding the sum of a set of data and dividing the sum by the number of pieces of data in the set
 Median – the middle number of a set of data that has been arranged in order from greatest to least or least to greatest
 Mode of numeric data – most frequent value in a set of data
 Measures of shape of a data distribution
 Range – the difference between the greatest number and least number in a set of data
 Interquartile range
 Shape of the data distribution
 Skewed right
 Mean usually greater than the median, and median greater than the mode
 Shape of the data has a tail to the right when graphed
 Symmetric
 Mean, median, and mode usually approximately the same
 Shape of the data resembles a bell curve when graphed
 Skewed left
 Mean usually less than the median, and median less than the mode
 Shape of the data has a tail to the left when graphed
 Comparisons of shapes, centers, and spreads
 Comparative dot plots
 Comparative box plots
Note(s):
 Grade Level(s):
 Grade 6 represented numeric data graphically, including dot plots, stemandleaf plots, histograms, and box plots.
 Grade 6 used the graphical representation of numeric data to describe the center, spread, and shape of the data distribution.
 Grade 6 summarized numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and used these summaries to describe the center, spread, and shape of the data distribution.
 Grade 8 will determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 VI. Statistical Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

7.12B 
Use data from a random sample to make inferences about a population.
Supporting Standard

Use
DATA FROM A RANDOM SAMPLE TO MAKE INFERENCES ABOUT A POPULATION
Including, but not limited to:
 Data – information that is collected about people, events, or objects
 Limitations
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Fractions
 Percents
 Inference – a conclusion or prediction based on data
 Size of hte sample influences the strength of the inference regarding the population
 Population – total collection of persons, objects, or items of interest
 Sample – a subset of the population selected in order to make inferences about the entire population
 Random sample – a subset of the population selected without bias in order to make inferences about the entire population
 Random samples are more likely to contain data that can be used to make predictions about a whole population.
 Data from a random sample given or collected in various forms
 Verbal
 Tabular (vertical/horizontal)
 Graphical
 Inferences based on random sample
 Qualitative – a broad subjective description (e.g., the probability of an event occurring is certain, more likely, not likely, equally likely, or impossible.)
 Quantitative – a narrowed objective description associated with a quantity (e.g., the probability of selecting a consonant from the word EXPERIMENT is 1.5 times as likely as selecting a vowel from the same word, etc.)
 Statistical analysis of data in a random sample to make inferences about a population
Note(s):
 Grade Level(s):
 Grade 7 introduces using data from random samples to make inferences about a population.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 IV. Measurement Reasoning
 VI. Statistical Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

7.12C 
Compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations.
Supporting Standard

Compare
TWO POPULATIONS BASED ON DATA IN RANDOM SAMPLES FROM THESE POPULATIONS, INCLUDING INFORMAL COMPARATIVE INFERENCES ABOUT DIFFERENCES BETWEEN THE TWO POPULATIONS
Including, but not limited to:
 Data – information that is collected about people, events, or objects
 Limitations
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Fractions
 Percents
 Inference – a conclusion or prediction based on data
 Size of the sample influences the strength of the inference regarding the population
 Population – total collection of persons, objects, or items of interest
 Sample – a subset of the population selected in order to make inferences about the entire population
 Random sample – a subset of the population selected without bias in order to make inferences about the entire population
 Random samples are more likely to contain data that can be used to make predictions about a whole population.
 Data from a random sample given or collected in various forms
 Verbal
 Tabular (vertical/horizontal)
 Graphical
 Informal comparative inferences based on random samples from two populations
 Qualitative – a broad subjective description (e.g., the probability of an event occurring is certain, more likely, not likely, equally likely, or impossible.)
 Quantitative – a narrowed objective description associated with a quantity (e.g., the probability of selecting a consonant from the word EXPERIMENT is 1.5 times as likely as selecting a vowel from the same word, etc.)
 Statistical analysis of data from random sample to make inferences about two populations
 Comparison of two populations
 Comparison of the shape, center, and spread of data from random samples using comparative dot plots and comparative box plots
Note(s):
 Grade Level(s):
 Grade 7 introduces comparing two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations.
 Grade 8 will simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 VI. Statistical Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation

7.13 
Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:


7.13B 
Identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget.
Supporting Standard

Identify
THE COMPONENTS OF A PERSONAL BUDGET, INCLUDING INCOME; PLANNED SAVINGS FOR COLLEGE, RETIREMENT, AND EMERGENCIES; TAXES; AND FIXED AND VARIABLE EXPENSES
Including, but not limited to:
 Budget – a monthly or yearly spending and savings plan for an individual, family, business, or organization
 Budgets based on financial records help people plan and make choices about how to spend and save their money
 Components of a personal budget
 Income – money earned or received
 Savings for college – money saved for continuing education beyond high school
 Savings for retirement – money saved over the period of time an individual is employed to be spent once the individual retires from their occupation
 Savings for emergencies – money saved for unexpected expenses (e.g., car repairs, emergency healthcare, etc.)
 Taxes – money paid to local, state, and federal governments to pay for things the government provides to its citizens
 Various types of taxes
 Income tax – a percentage of money paid on the earned wages of an individual or business for the federal and/or state governments as required by law
 Payroll tax – a percentage of money that a company withholds from its employees for the federal government as required by law
 Sales tax – a percentage of money collected by a store (retailer), in addition to a good or service that was purchased, for the local government as required by law
 Property tax – a percentage of money collected on the value of a property for the local government as required by law
 Expense – payment for goods and services
 Fixed expenses – expenses that are consistent from month to month
 Variable expenses – expenses that vary in cost from month to month
Calculate
WHAT PERCENTAGE EACH CATEGORY OF A PERSONAL BUDGET COMPRISES OF THE TOTAL BUDGET
Including, but not limited to:
 Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
 Various forms of positive rational numbers
 Counting (natural) numbers
 Decimals
 Percents
 Proportional reasoning to determine percentages within a budget
 Proportional reasoning to determine amounts within a budget
Note(s):
 Grade Level(s):
 Grade 5 balanced a simple budget.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 TxCCRS:
 I. Numeric Reasoning
 VIII. Problem Solving and Reasoning
 IX. Communication and Representation
 X. Connections
